Finite Group Databasebeta

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C11⋊C5×(C49⋊C3)⋊C4 #44568333

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×(C49⋊C3)⋊C4
unambiguous semidirect product(C49⋊C3)⋊(C4×C11⋊C5)
unambiguous semidirect productDic49⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×(C49⋊C3)⋊C4)⋊C5
unambiguous semidirect product(C11⋊C5×Dic49)⋊C3

Splittings

derived, HallC11×C49 ⋊ C3×C4×C5
HallC11⋊C5×Dic49 ⋊ C3
HallC11⋊C5×C49⋊C3 ⋊ C4
HallC11×(C49⋊C3)⋊C4 ⋊ C5
HallC49×C11⋊C5 ⋊ C3×C4
HallC11×Dic49 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C4×C5
HallDic49 ⋊ C3×C11⋊C5
HallC49⋊C3 ⋊ C4×C11⋊C5
SylowC49 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C5×(C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D49⋊C3
commutator, hypocenterC11×C49C3×C4×C5
FrattiniC2×C7AGL(1,𝔽7)×C11⋊C5
Fitting, cosocleC2×C11×C49C2×C3×C5
socleC2×C7×C11C5×AGL(1,𝔽7)
prime radicalC2×C11⋊C5×C49⋊C3C2
LCSG ▷ C11×C49
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 35);